Self-study questions – Ch. 5

Pressure-volume work

The following questions are drawn from pp.123-128 :
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1. Be able to remember and correctly use equations (5.8) and (5.9).

2. Does w describe the amount of work per unit mass done on or by the parcel? What about -w?

3. Be able to explain what’s going on in Fig. 5.2, both mathematically (e.g., using the appropriate integrals) and in words.

4. What is the significance of a closed cycle? How, if at all, is the state of the parcel different at the end of one or more repeats of the cycle than it was at the beginning?

5. Can the amount of net work done by a parcel be non-zero for a closed cycle?

6. What is the relationship between the sign of the net work done by a parcel and the direction (clockwise or counterclockwise) of the closed cycle as depicted on a pressure-volume diagram? What does the amount of work correspond to on such a diagram?

First Law of Thermodynamics

The following questions are drawn from pp. 129-135:
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1. Be able to state the First Law in words, using something similar to either of the two formulations in the list just above the middle of p. 130.

2. Be able to identify each of the terms in (5.13).

3. Be able to explain the concept of the heat capacity (or specific heat) of a material in words and giving the appropriate units.

4. Be able to write down from memory equations (5.17), (5.18), (5.25), and (5.26). Which of these are valid only for an ideal gas, and why?

5. Be able to write down all of the special cases of the First Law given in (5.28)-(5.32), starting with one of the two versions of (5.27).

6. Be able to comfortably determine (i) work done and (ii) heat added for a particular process, using reasoning similar to that required in Prob. 5.4. Reminder: Your first task is always to specify the solution in symbolic terms.

Dry adiabatic processes

The following questions are drawn from pp. 136-141:
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1. Be able to derive Eq. (5.36), starting with the appropriate form of the 1st Law.

2. Be able to explain in words what Poisson’s Equation does — that is, for what kind of process it is used. Be able to perform the appropriate calculation for a given starting and/or ending temperature and/or pressure.

3. Be able to explain the meaning and/or physical significance of potential temperature and how Poisson’s Equation is used to compute it.

4. Be able to identify dry adiabats on a Skew-T diagram and to explain under what circumstances they describe the behavior of parcels of air. Given a blank graph with temperature as the x-axis and pressure as the y-axis, how would you go about accurately plotting a dry adiabat?

5. Be able to reproduce the derivation of (5.46). In particular, state the major assumptions or approximations that go into the derivation.

6. We looked at two ways of calculate dry adiabatic changes in temperature: one for a particular starting and ending pressure (Poisson’s equation), the other for a given change in altitude z (the dry adiabatic lapse rate). Which one is fundamentally more direct and accurate, and why? Under what conditions will one of the two relationships be less accurate?

Heat Engines

The following questions are drawn from pp. 142-151:
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1. Be able to explain the balance the must exist between net work done by a parcel and net heat added to the parcel.

2. Given a) the head added, b) the heat lost, and c) the work done during a cyclic process determine the efficiency of the process at converting heat to work.

3. Describe the four “legs” of the so-called Carnot heat engine.

4. Given appropriate information about the starting and ending states of a parcel of air during each leg of a Carnot cycle, be able to compute the heat added and the work done during that leg.

5. Given a reversible heat engine that passes heat from a warm reservoir at temperature T2 to cooler reservoir T1, determine the maximum possible efficiency, defined as “work done” divided by “heat added.”

6. Be able to explain the difference between a reversible and irreversible process and why that difference matters.

 

Enthalpy and dry static energy

The following questions are drawn from pp. 151-154:
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1.  Know the definition of enthalpy and how it relates to one of the two common forms of the 1st Law of Thermodynamics.

2. Under what condition(s) is  the amount of heated added to a parcel of air equal to the change of enthalpy?

3. What quantity is conserved for dry adiabatic motions in the atmosphere, and how is that quantity defined?

4. Be able to derive the dry adiabatic lapse rate from conservation of dry static energy.

 

Miscellaneous applications

The following questions are drawn from pp. 154-160 :

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1. Be able to explain the process by which an temperature inversion results from an adiabatically subsiding layer of air.

2. Be able to identify the four major diabatic processes and discuss when/where/how they are relevant.

3. Given specific information about a diabatic process, be able to determine the heat added (or rate of heat added) per unit mass so as to be able to determine the change of temperature (or rate of change of temperature) and/or work done using the 1st Law.

4. Demonstrate that you understand the relationship between area and energy (e.g., work) on a Skew-T diagram, including the sign.